Retroreflective sheeting for projector-based display system

ABSTRACT

Provided herein is a retroreflective article comprising a retroreflective film and a plurality of isosceles triangular pyramid prisms embossed on the back surface of the retroreflective film. The prisms are configured such that the article reflects an incident light beam into two reflected light beams that are offset from and on opposite sides of the incident light beam. The two reflected light beams can provide two viewing zones located at different positions relative to the incident light beam source.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.62/551,288, filed Aug. 29, 2017, which is incorporated by reference inits entirety herein for all purposes.

FIELD

The present disclosure relates generally to prismatic retroreflectivefilms that can be used, for example and without limitation, asprojection screens.

BACKGROUND

Retroreflectors in the form of sheeting are often used in diverseapplications including projector screens, traffic signs, and safetygarments for road construction workers. In each of these cases, apurpose of the retroreflector is to increase or direct the visibility ofreflected light. Retroreflective sheeting can comprise a layer oftransparent plastic material having a substantially smooth frontsurface, and a rear surface provided with a plurality of retroreflectiveelements. Conventional retroreflectors use these elements to reflect anangular cone of light back towards the source. The angular spread of thecone is determined by the properties of the retroreflector. The returnedlight typically is brighter close to the source (at smaller observationangles), and falls off farther from the source (at larger observationangles).

An example of a retroreflector can be found in International PatentApplication Publication No. WO 99/15920, which describes a reflectivearticle having a structured surface which includes a plurality ofreflective elements, each having a first, second, and third mutuallyreflecting face with definable dihedral angles. At least one of thedihedral angles differs from a right angle by more than two degrees. Inone embodiment exactly one of the dihedral angles is so characterizedand the remaining dihedral angles differ from a right angle by less thantwo degrees. In one embodiment the reflective elements are bounded by aplurality of groove sets in the structured surface, the groove setshaving a preferred groove spacing between about 0.0004 and 0.002 inches(10-50 μm). Reflective elements having different sets of dihedral anglescan be incorporated in the structured surface by tiling or by providingone or more sequences of grooves with differing groove side angle pairs.The article reflects an obliquely incident beam of light into tworeflected beams on opposed sides of the incident beam. One of the twobeams has a beam width sufficient to illuminate a predefined observationzone angularly displaced from the incident light direction.

The cube-corner retroreflective article of U.S. Pat. No. 4,775,219includes three lateral reflecting faces formed by three intersectingsets of parallel V-shaped grooves, with at least one of the setsincluding, in a repeating pattern, at least two groove side angles thatdiffer from one another. Thereby the array of cube-cornerretroreflective elements is divided into repeating sub-arrays that eachcomprise a plurality of cube-corner retroreflective elements in aplurality of distinctive shapes that retroreflect incident light indistinctively shaped light patterns.

The display system of U.S. Patent Application Publication No. US2017/0160631 comprises a retro-reflective screen having retro-reflectivescreen elements that reflect incident light. Each of theretro-reflective screen elements can include three intersecting planes.At least one of the three intersecting planes intersects an adjacentplane at an angle that is 90 degrees with an offset greater than 0degrees. The display system can further include at least one projectorthat projects the light onto the retro-reflective screen, which lightcharacterizes an image or video. The retroreflective screen having theretro-reflective screen elements can reflect the light at a cross-talkthat is decreased by at least 10% and/or an intensity that is increasedby at least 5%, as compared to a retro-reflective screen withretro-reflective screen elements having planes that each intersect anadjacent plane at an angle of 90° without the offset.

Even in view of these references, the need exists for retroreflectivesheeting that can be used in a projector-based display for the focuseddirection of reflected images to multiple viewing positions located atdifferent positions relative to the projector.

SUMMARY

In one embodiment, the disclosure is to a retroreflective article thatcomprises a retroreflective film and a plurality of retroreflectiveelements disposed on the back surface of the retroreflective film. Eachof the retroreflective elements can be a non-equilateral triangularpyramid prism. The prisms can be bounded by three intersecting sets ofsubstantially parallel and v-shaped grooves. Each groove side of thegrooves forms a half angle, wherein at least one of the half anglespreferably ranges from 43.5 degrees to 45 degrees, from 25 degrees to 30degrees, or from 25 degrees to 28.5 degrees. The prisms can have threetriangular faces and a triangular base with two sides that differ inlength from one another. Preferably, the ratio of the length of thesmaller of these two sides to the length of the larger of the two sidesranges from 80% to 92.5%. The prisms can have a third dihedral angleerror with a magnitude that is greater than 1 degree, e.g., the thirddihedral angle error can be less than −1 degree or greater than 1degree. In certain aspects, each prism is canted edge-more-parallel at acant angle greater than 0 degrees.

In another embodiment the disclosure relates to a display system. Thedisplay system comprises a retroreflective article in accordance with anembodiment, a projector, and a computer processor. The projector isconfigured to direct an incident light beam towards the retroreflectivearticle. The retroreflective article is configured to reflect theincident light beam into a first and second reflected light beam thatare offset from and on opposite sides of the incident light beam. Thecomputer system can perform operations comprising controlling theprojector to direct the incident light beam towards the retroreflectivearticle.

In another embodiment the disclosure relates to a method of displayingan image. The method comprises providing a retroreflective article inaccordance with an embodiment, and a projector. The method furthercomprises controlling the projector to direct an incident light beamtowards the retroreflective article, thereby reflecting the incidentlight beam into a first and second reflected light beam offset from andon opposite sides of the incident light beam.

BRIEF DESCRIPTION OF DRAWINGS

The embodiments are described in detail below with reference to theappended drawings, wherein like numerals designate similar parts.

FIG. 1 is a top view of a retroreflective element of a retroreflectivearticle in accordance with an embodiment.

FIG. 2 is a plot of the positions of two narrow light beams returned bya retroreflective article in accordance with an embodiment.

FIG. 3 is a plot of the positions of two broadened light beams returnedby a retroreflective article having adjusted dihedral angles inaccordance with an embodiment.

FIG. 4 is a plot of the positions of two vertically spread light beamsreturned by a retroreflective article having a diffusing film inaccordance with an embodiment.

FIG. 5A is an illustration of the cutting of the first grooves in thesurface of a substrate in accordance with an embodiment.

FIG. 5B is an illustration of the cutting of the second grooves in thesurface of a substrate in accordance with an embodiment.

FIG. 5C is an illustration of the cutting of the third grooves in thesurface of a substrate in accordance with an embodiment.

FIG. 5D is a plan view of an array of cube corner prisms bounded by thefirst, second, and third grooves in the surface of a substrate or theback surface of a retroreflective film in accordance with an embodiment.

FIG. 6 is a plot of retroreflective efficiency versus third groove halfangle for a retroreflective article having positive or negative majordihedral angle aberrations.

FIG. 7 is a series of plots of retroreflective efficiency versushorizontal and vertical entrance angles for various third groove halfangles.

FIG. 8 is a plot of retroreflective efficiency versus horizontalentrance angle for various third groove half angles.

FIG. 9A is a plot of a viewing zone superimposed with the position of alight beam returned by a retroreflective article having a 6-degreeoffset, a 29.5-degree third groove half angle, and a diffusing film. Theincident light enters the article head-on.

FIG. 9B is a plot of a viewing zone superimposed with the position of alight beam returned by the article of FIG. 9A. The incident light entersthe article with a direction tilted 20 degrees to the right of, and 15degrees below, the head-on direction.

FIG. 10A is a plot of a viewing zone superimposed with the position of alight beam returned by a retroreflective article having a 6-degreeoffset, a 44.5-degree third groove half angle, and a diffusing film. Theincident light enters the article head-on.

FIG. 10B is a plot of a viewing zone superimposed with the position of alight beam returned by the article of FIG. 10A. The incident lightenters the article with a direction tilted 20 degrees to the right of,and 15 degrees below, the head-on direction.

FIG. 11A is a plot of a viewing zone offset 0.3 m behind the projectorsuperimposed with the position of a light beam returned by aretroreflective article having a 6-degree offset, a 29.5-degree thirdgroove half angle, and a diffusing film. The incident light enters thearticle head-on.

FIG. 11B is a plot of a viewing zone offset 0.3 m behind the projectorsuperimposed with the position of a light beam returned by the articleof FIG. 11A. The incident light enters the article with a directiontilted 20 degrees to the right of, and 15 degrees below the head-ondirection.

FIG. 12 presents top-down illustrations of viewing retroreflectivearticles having an HG3 value in the range from 40 degrees to 45 degreesfrom a position offset behind a projector.

FIG. 13 is a plot of the positions of two vertically asymmetrical lightbeams returned by a retroreflective article having dihedral angle errorsthat are not balanced.

DETAILED DESCRIPTION

The present disclosure generally relates to retroreflective screens thatprovide advantageous combinations of performance characteristics, forexample, when the screens are employed in projector-based displays. Forexample, the inventors have determined that it is beneficial for ascreen to reflect light back preferentially, or almost exclusively, tospecific viewing regions located at different positions relative to aprojector, e.g., above and below the projector, that is the source ofthe incident light being reflected. Existing projection screens,however, typically either scatter light in all directions or send lightback somewhat preferentially in the general direction of the projector.Thus, with conventional retroreflective screens, it is often difficultto control the return of light to particular viewing regions in such away that the reflected light: 1) can be easily observed from twodifferent predetermined viewing regions, but 2) cannot be easilyobserved from outside of these regions.

The inventors have now discovered particular configurations ofretroreflective elements that achieve both of these results. Forexample, the introduction of specific aberrations into the dihedralangles of cube corner retroreflective elements can beneficially causelight to deviate from perfect retroreflection. It has been discoveredthat by carefully controlling the configurations of the retroreflectiveelements arrayed on the screen, these deviations produce the desiredreflection divergence patterns with two distinct viewing zones. Thesedivergence patterns advantageously allow for applications in which thecontent viewed on the screen can depend strongly on the position of theviewer relative to the screen and the projector. For example, twoviewers located above and below a projector could view the same contenton the screen, while two other viewers at different locations above andbelow a different projector could view entirely different content on thesame screen. In addition, the inventive retroreflective screens alsoallow for very bright images in the viewing regions, since light is notwasted by scattering in all directions. Other benefits of theretroreflective articles or screens include a transparent appearance tothe film, and relative uniformity of brightness across the screen andwithin the multiple viewing regions. For example, certain configurationsof the provided retroreflective screens can compensate for horizontalbrightness instabilities typically associated with viewing positionsoffset towards or away from the screen.

In particular, it has been found that a retroreflective articlecomprising a retroreflective film and a plurality of specificretroreflective elements disposed, e.g., embossed, on the back surfaceof the retroreflective film can achieve the surprising results mentionedabove. For example, the retroreflective elements can be configured toreflect an incident light beam such that the majority of reflected lightis divided into a first reflected light beam and a second reflectedlight beam. The retroreflective article (or the components thereof) canbe configured such that at least 30%, e.g., at least 40%, at least 50%,at least 60%, at least 70%, at least 75%, at least 80%, at least 85%, atleast 90%, at least 92%, at least 94%, at least 96%, at least 97%, atleast 98%, or at least 99% of the reflected light is divided into thefirst and second reflected light beams. The incident light beam canoriginate from a light source that emits light at least in the directionof the retroreflective article. In a preferred embodiment, the incidentlight beam originates from a projector having an optical axis that isdirected towards the retroreflective article or screen.

The first and second reflected light beams reflected by theretroreflective article are directed to (at least) two differentlocations, e.g., on different (opposite) sides of the incident lightbeam. In a preferred embodiment, the incident light beam originates froma projector, the retroreflective article is oriented substantiallyvertically, and the first and second reflected light beams are directedto viewing regions or zones that are above and below the location of theprojector. The first reflected light beam may be offset from theincident light beam by a first reflected light angle that is greaterthan 1 degree, e.g., greater than 2 degrees, greater than 3 degrees,greater than 4 degrees, greater than 5 degrees, greater than 6 degrees,greater than 7 degrees, greater than 8 degrees, greater than 9 degrees,greater than 10 degrees, greater than 12 degrees, greater than 14degrees, greater than 16 degrees, greater than 18 degrees, greater than20 degrees, greater than 25 degrees, greater than 30 degrees, greaterthan 35 degrees, greater than 40 degrees, or greater than 45 degrees.The first reflected light angle can range from 1 degree to 45 degrees,e.g., from 1 degree to 25 degrees, from 5 degrees to 30 degrees, from 10degrees to 35 degrees, from 15 degrees to 40 degrees, or from 25 degreesto 40 degrees. The first reflected light angle can range from 1 degreeto 10 degrees, e.g., from 1 degree to 6 degrees, from 2 degrees to 7degrees, from 3 degrees to 8 degrees, from 4 degrees to 9 degrees, orfrom 5 degrees to 10 degrees.

The second reflected light beam can be offset from the incident lightbeam by a second reflected angle having a magnitude substantiallyidentical to that of the first reflected angle, and a directiondifferent from, e.g., opposite of, that of the first reflected lightbeam relative to the incident light beam. The limits and rangesdiscussed above for the first reflected angle are applicable to thesecond reflected angle. In one embodiment, the first reflected lightangle is greater than 4 degrees above the incident light beam (at anoffset angle of 4 degrees), and the second reflected light angle isgreater than 4 degrees below the incident light beam (at an offset angleof −4 degrees). The first and second reflected light angles can be, forexample, greater than 5 degrees, greater than 6 degrees, greater than 7degrees, greater than 8 degrees, greater than 9 degrees, greater than 10degrees, greater than 12 degrees, greater than 14 degrees, greater than16 degrees, greater than 18 degrees, greater than 20 degrees, greaterthan 25 degrees, greater than 30 degrees, greater than 35 degrees,greater than 40 degrees, or greater than 45 degrees above and below theincident light beam, respectively. In this coordinate system, lightreturning directly to the light source would have α_(x)=0 degrees andα_(y)=0 degrees, wherein the term a is used to refer to the observationangle, i.e., the angle between the observed retroreflected beam and theincident light beam. The terms α_(x) and α_(y) refer to orthogonalcomponents of the observation angle α, wherein α_(y) lies in a verticalplane.

As used herein, the term “angle having a magnitude substantiallyidentical” refers to a relationship between two angles wherein theabsolute values of the angles are within 5 degrees of one another. Forexample, two angles have a magnitude substantially identical to oneanother if the absolute values of the angles are within 4 degrees,within 3 degrees, within 2 degrees, within 1 degree, within 0.9 degrees,within 0.8 degrees, within 0.7 degrees, within 0.6 degrees, within 0.5degrees, within 0.4 degrees, within 0.3 degrees, within 0.2 degrees, orwithin 0.1 degrees of one another.

In some embodiments, the first reflected light beam has a brightnessthat is substantially identical to that of the second reflected lightbeam. This feature allows viewers positioned in the viewing zones orregions associated with each of the two viewing zones or regions toobserve on the screen an image with substantially the same lightintensity. As used herein, the term “brightness that is substantiallyidentical” refers to a relationship between two brightness valueswherein the first brightness value is within 20% of the secondbrightness value. For example, two brightness values are substantiallyidentical if the first brightness value is within 18%, within 16%,within 14%, within 12%, within 10%, within 9%, within 8%, within 7%,within 6%, within 5%, within 4%, within 3%, within 2%, or within 1% ofthe second brightness value. In some embodiments, the first reflectedlight beam has a brightness that is not substantially identical to thatof the second reflected light beam.

The retroreflective film has a front surface and a back surface that isopposite the front surface. The front surface can be substantiallysmooth. As used herein, the term “substantially smooth” refers to anouter surface that is completely or mostly free of texturing such asvoids, protrusions, grooves, or ridges. A surface can have minorindentations or raised portions, or other imperfections not intendedduring manufacture, and still be considered to be substantially smooth.In a preferred embodiment, the front surface is substantially planar. Itis appreciated, however, that the front surface can alternatively have acurved or otherwise nonplanar geometry for at least a portion of itsshape.

The material of the retroreflective film can vary widely. For examplethe material of the retroreflective film can be a transparent plasticmaterial, such as a polymer. The material can be selected from a widevariety of polymers, including, but not limited to, polycarbonates,polyesters, polystyrenes, polyarylates, styrene-acrylonitrilecopolymers, urethane, acrylic acid esters, cellulose esters,ethylenically unsaturated nitrites, hard epoxy acrylates, acrylics andthe like, with acrylic and polycarbonate polymers being preferred. Insome embodiments, the retroreflective film comprises acrylic. In someembodiments, the retroreflective film comprises polycarbonate. In someembodiments, the retroreflective film comprises both acrylic andpolycarbonate. In certain aspects, the retroreflective film includes aprism layer and a cap layer, wherein the prism layer comprises one ofacrylic or polycarbonate, and wherein the cap layer comprises the otherof acrylic or polycarbonate.

In a preferred embodiment, the retroreflective article further comprisesa plurality of retroreflective elements disposed, e.g., embossed, on theback surface of the retroreflective film. It is appreciated, however,that the plurality of retroreflective elements can alternatively bedisposed on the front surface of the retroreflective film, and thediscussion relating to the retroreflective elements disposed on the backsurface is applicable to retroreflective elements disposed on the frontsurface. The composition of the retroreflective elements can varywidely. For example the retroreflective elements can comprise metal,e.g., can be metallized. In a preferred embodiment, the retroreflectiveelements are air-backed. The use of air-backed retroreflective elementscan give a semi-transparent or translucent character to theretroreflective film and the retroreflective article or screen.

In some embodiments, the retroreflective elements each have the shape ofa non-equilateral triangular pyramid prism, e.g., an isoscelestriangular pyramid prism, and each prism comprises multiple faces and abase. The triangular shape of each prism face and base can benon-equilateral, e.g., isosceles. Each of the prisms can be canted, andcan have a triangular base that can be in the shape of an isoscelestriangle. For an isosceles triangle-based pyramid prism, two of thethree faces have substantially the same shape and size. Each triangularface and base comprises three sides. In some embodiments, two of thethree triangular base sides differ in length such that the ratio of thelength of the smaller side to the length of the larger side ranges from80% to 92.5%, e.g., from 80% to 87.5%, from 81.25% to 88.75%, from 82.5%to 90%, from 83.75% to 91.25%, or from 85% to 92.5%. In someembodiments, the ratio of the smaller side length to the larger sidelength ranges from 83% to 90%, e.g., from 83% to 87.2%, from 83.7% to87.9%, from 84.4% to 88.6%, from 85.1% to 89.3%, or from 85.8% to 90%.In terms of lower limits, the ratio of the length of the smaller side tothe length of the larger side can be at least 80%, at least 81.25%, atleast 82.5%, at least 83.75%, at least 85%, at least 86.25%, at least87.5%, at least 88.75%, at least 90%, or at least 91.25%. In terms ofupper limits, the ratio of the length of the smaller side to the lengthof the larger side can be less than 92.5%, less than 91.25%, less than90%, less than 88.75%, less than 87.5%, less than 86.25%, less than 85%,less than 83.75%, less than 82.5%, or less than 81.25%.

FIG. 1 illustrates a top view of one of the plurality of non-equilateraltriangular pyramid prisms. The prisms are each in the shape of a cubecorner, and can also be referred to as cube corner prisms. The prism 100has a first 101, second 102, and third 103 triangular face thatintersect at an apex 104 configured to point away from the back surfaceof the retroreflective film. Three dihedral angles 105, 106, and 107 areformed between faces 101 and 102, between faces 101 and 103, and betweenfaces 102 and 103, respectively. If the triangular pyramid prism has theshape of an orthogonal cube corner, then each of the dihedral angles is90 degrees.

The term “dihedral angle error” as used herein refers to the differencebetween the actual dihedral angle and 90 degrees. Each non-equilateraltriangular pyramid prism has three dihedral angle errors—first dihedralangle error (e₁), a second dihedral angle error (e₂), and a thirddihedral angle error (e₃). The third dihedral angle error (e₃) isdefined as the dihedral angle error between the two faces with similar,but mirrored (i.e., substantially congruent) shape. As used herein, theterm “substantially congruent” refers to a relationship betweendifferent shapes wherein the lengths of analogous sides of the differentshapes differ from one another by less than 20% (e.g., less than 18%,less than 16%, less than 14%, less than 12%, less than 10%, less than8%, less than 6%, less than 4%, or less than 2%), and the analogousinterior angles of the different shapes differ from one another by lessthan 20% (e.g., less than 18%, less than 16%, less than 14%, less than12%, less than 10%, less than 8%, less than 6%, less than 4%, or lessthan 2%).

The inventors have found that the offset of the first and secondreflected light beams relative to the incident light beam is a functionof the prism dihedral angles, and that these reflected light beams canbe controlled by aberrating the prism dihedral angles. If the base ofthe isosceles triangle is oriented vertically, then by configuring thedihedral angle between the two substantially congruent faces to differsignificantly from the nominal value of 90 degrees (i.e., setting e₃ todiffer significantly from zero), the returning beam can be divided intotwo narrow reflected beams, with one deviating upwards and the otherdownwards. FIG. 2 shows a graph of the positions of two such deviatedbeams retroreflected by an array of cube corner isosceles triangleprisms. In some cases, it is desirable that the reflected light beamsare not as narrow as shown in FIG. 2, but are instead broadened as shownin FIG. 3. Such reflected beams can be achieved via control of thedihedral angles of the prisms, as discussed in more detail below.

As discussed above, each prism has three dihedral angles, with the thirddihedral angle defined as the dihedral angle between the prism faceshaving mirrored similar shapes. In some embodiments, the average of thethird dihedral angle errors of all prisms of the retroreflective elementarray is less than 0 degrees. The average of the third dihedral angleerrors can range, for example and without limitation, from 0 degrees to−10 degrees, e.g., from 0 degrees to −6 degrees, from −1 degrees to −7degrees, from −2 degrees to −8 degrees, from −3 degrees to −9 degrees,or from −4 degrees to −10 degrees. The average of the third dihedralangle errors can range from 0 degrees to −4 degrees, e.g., from 0degrees to −2.4 degrees, from −0.4 degrees to −2.8 degrees, from −0.8degrees to −3.2 degrees, from −1.2 degrees to −3.6 degrees, or from −1.6degrees to −4 degrees. In terms of lower limits, the average of thethird dihedral angle errors can be greater than −10 degrees, greaterthan −9 degrees, greater than −8 degrees, greater than −7 degrees,greater than −6 degrees, greater than −5 degrees, greater than −4degrees, greater than −3 degrees, greater than −2 degrees, or greaterthan −1 degrees. In terms of upper limits, the average of the thirddihedral angle errors can be less than −1 degree, less than −2 degrees,less than −3 degrees, less than −4 degrees, less than −5 degrees, lessthan −6 degrees, less than −7 degrees, less than −8 degrees, or lessthan −9 degrees. Large negative values of e3 can be used to achieve thepattern of offset retroreflected light beams. A similar offset can beachieved with large positive values of e₃, but the use of negativevalues, as opposed to positive values, can give an efficiency boost tothe cube corner prisms, as discussed in more detail below.

In some embodiments, the average of the first and/or second dihedralangle errors of all prisms of the retroreflective element array has amagnitude that is less than 0.5 degrees, e.g., less than 0.4 degrees,less than 0.3 degrees, less than 0.2 degrees, or less than 0.1 degrees.In some embodiments, the average of the first and/or second dihedralangle errors of all prisms of the retroreflective element array has amagnitude that is greater than 0.01 degrees, e.g., greater than 0.1degrees, greater than 0.2 degrees, greater than 0.3 degrees, or greaterthan 0.4 degrees. The average of the first and/or second dihedral angleerrors can, for example, range from 0 degrees to 0.3 degrees, from 0.05degrees to 0.35 degrees, from 0.1 degrees to 0.4 degrees, from 0.15degrees to 0.45 degrees, or from 0.2 degrees to 0.5 degrees.

In some embodiments, the magnitude of each dihedral angle error of eachprism of the retroreflective element array ranges from 0.01 degrees to10 degrees. The magnitude of each dihedral angle error can range, forexample and without limitation, from 0.01 degrees to 6 degrees, from 1degrees to 7 degrees, from 2 degrees to 8 degrees, from 3 degrees to 9degrees, or from 4 degrees to 10 degrees. The magnitude of each dihedralangle error can range from 0.01 degrees to 4 degrees, e.g., from 0.01degrees to 2.4 degrees, from 0.4 degrees to 2.8 degrees, from 0.8degrees to 3.2 degrees, from 1.2 degrees to 3.6 degrees, or from 1.6degrees to 4 degrees. In terms of upper limits, the magnitude of eachdihedral angle error can be less than 10 degrees, e.g., less than 9degrees, less than 8 degrees, less than 7 degrees, less than 6 degrees,less than 5 degrees, less than 4 degrees, less than 3 degrees, less than2 degrees, or less than 1 degrees. In terms of lower limits, themagnitude of each dihedral angle error can be greater than 0.01 degrees,e.g., greater than 1 degree, greater than 2 degrees, greater than 3degrees, greater than 4 degrees, greater than 5 degrees, greater than 6degrees, greater than 7 degrees, greater than 8 degrees, or greater than9 degrees.

Alternatively or additionally, broadening the reflected light beams canbe accomplished with the use of a diffusing film. A diffusing film canbe located, for example, directly adjacent to the front surface of theretroreflective film. In some embodiments, an adhesive layer is employedto adhere the diffusing film to the front surface. In these cases, theadhesive layer can be directly adjacent to the front surface of theretroreflective film, and the diffusing film can be directly adjacent tothe adhesive layer, e.g., the adhesive layer can be sandwiched betweenthe diffusing film and the retroreflective film. In some embodiments,one or more other films or layers are positioned between the diffusingfilm and the front surface of the retroreflective film. In someembodiments, the diffusing film is itself a component layer of theretroreflective film, and is located between the front and back surfacesof the retroreflective layer.

The diffusing film can comprise light-diffusing particles dispersed in amatrix material, wherein the light-diffusing particles have a refractiveindex that is different from the refractive index of the matrix. Thelight-diffusing particles can vary in color, e.g., can be white orblack, or substantially white or substantially black, with other colorsbeing contemplated as well. The light-diffusing particles can betransparent, or substantially so. The light-diffusing particles cancomprise particles selected from the group consisting of white particlesor particles that are substantially white, black particles or particlesthat are substantially black, transparent particles or particles thatare substantially transparent, and combinations thereof. For highrefractive index applications, e.g., those having indices of refractionvalues of 1.6 to 2.8, the light-diffusing particles can comprisetitanium oxide (TiO₂), silicon dioxide (SiO₂), calcium carbonate(CaCO₃), barium sulfate (BaSO₄), or combinations thereof. In embodimentswhere the light-diffusing particles have a smaller indices ofrefraction, e.g., those having index of refraction values of 1.0 to 1.5,the light-diffusing particles can include a material comprising anorganic or inorganic compound such as, for example, silicone resin,polytetrafluoroethylene (PTFE), roughened quartz, flashed opal, orcombinations thereof. The light-diffusing particles can include hollowstructures or hollow particles such as hollow glass beads or hollowresin beads, or hollow structures made from other materials.

In certain aspects, the diffusing film is a structured diffuser, e.g., adiffuser comprising a patterned surface. In some embodiments, thepatterned surface of the diffuser is a holographically generated reliefpattern. The structured or patterned surface can be on the inner face ofthe diffuser, e.g., the diffuser surface facing the retroreflectivefilm, or on the outer face of the diffuser, e.g., the diffuser surfacefacing opposite the retroreflective film. The surface relief pattern ofthe diffuser can be anisotropic, such that the pattern is elliptical.Such an anisotropic surface relief pattern can be used to broaden thereflected light beams by differing degrees in different directions. Insome embodiments, the diffusing film comprises an anisotropic surfacerelief pattern configured to reflect light with a greater angle ofdiffusion in the horizontal x direction than in the vertical ydirection. In some embodiments, the diffusing film comprises ananisotropic surface relief pattern configured to reflect light with agreater angle of diffusion in the vertical y direction than in thehorizontal y direction.

The diffusing film can have a full-width half-maximum angle of diffusionin a vertical y direction that is less than 2 degrees, e.g., less than1.8 degrees, less than 1.6 degrees, less than 1.4 degrees, less than 1.2degrees, less than 1 degree, less than 0.9 degrees, less than 0.8degrees, less than 0.7 degrees, less than 0.6 degrees, or less than 0.5degrees. The full-width half-maximum angle of diffusion in the ydirection can, for example, range from 0 degrees to 2 degrees, e.g.,from 0 degrees to 1.2 degrees, from 0.2 degrees to 1.4 degrees, from 0.4degrees to 1.6 degrees, from 0.6 degrees to 1.8 degrees, or from 0.8degrees to 2 degrees. The use of such a smaller vertical diffusion anglecan limit the vertical spread of the light. This can be useful, forexample, when it is desirable to return light for viewing at just oneheight. The diffusing film can have a full-width half-maximum angle ofdiffusion in a horizontal x direction that is greater than 1.5 degrees,e.g., greater than 1.8 degrees, greater than 2.1 degrees, greater than2.4 degrees, greater than 2.7 degrees, greater than 3 degrees, greaterthan 3.5 degrees, greater than 4 degrees, greater than 4.5 degrees, orgreater than 5 degrees. The full-width half-maximum angle of diffusionin the x direction can, for example, range from 0 degrees to 5 degrees,e.g., from 0 degrees to 3 degrees, from 0.5 degrees to 3.5 degrees, from1 degrees to 4 degrees, from 1.5 degrees to 4.5 degrees, or from 2degrees to 5 degrees. The use of such a larger horizontal diffusionangle can allow for multiple horizontal viewing positions. This can beuseful, for example, when accommodating multiple side-by-side viewers.In some embodiments, the diffusing film has a full-width half-maximumangle of diffusion in a vertical y direction that is less than 1 degree,and a full-width half-maximum angle of diffusion in a horizontal xdirection that is greater than 3 degrees.

The diffusing film can have a full-width half-maximum angle of diffusionin a horizontal x direction that is less than 2 degrees, e.g., less than1.8 degrees, less than 1.6 degrees, less than 1.4 degrees, less than 1.2degrees, less than 1 degree, less than 0.9 degrees, less than 0.8degrees, less than 0.7 degrees, less than 0.6 degrees, or less than 0.5degrees. The full-width half-maximum angle of diffusion in the xdirection can, for example, range from 0 degrees to 2 degrees, e.g.,from 0 degrees to 1.2 degrees, from 0.2 degrees to 1.4 degrees, from 0.4degrees to 1.6 degrees, from 0.6 degrees to 1.8 degrees, or from 0.8degrees to 2 degrees. The use of such a smaller horizontal diffusionangle can limit the horizontal spread of the light. This can be useful,for example, when it is desirable to return light for viewing by justone person. The diffusing film can have a full-width half-maximum angleof diffusion in a vertical y direction that is greater than 1.5 degrees,e.g., greater than 1.8 degrees, greater than 2.1 degrees, greater than2.4 degrees, greater than 2.7 degrees, greater than 3 degrees, greaterthan 3.5 degrees, greater than 4 degrees, greater than 4.5 degrees, orgreater than 5 degrees. The full-width half-maximum angle of diffusionin the y direction can, for example, range from 0 degrees to 5 degrees,e.g., from 0 degrees to 3 degrees, from 0.5 degrees to 3.5 degrees, from1 degrees to 4 degrees, from 1.5 degrees to 4.5 degrees, or from 2degrees to 5 degrees. The use of such a larger vertical diffusion anglecan allow for multiple vertical viewing positions. This can be useful,for example, when accommodating viewers with differing heights. In someembodiments, the diffusing film has a full-width half-maximum angle ofdiffusion in a horizontal x direction that is less than 1 degree, and afull-width half-maximum angle of diffusion in a vertical y directionthat is greater than 3 degrees.

FIG. 4 shows a graph of the positions of two deviated reflected lightbeams retroreflected by an article having a diffusion film with afull-width half-maximum angle of diffusion in a horizontal x directionof 0.8 degrees (FWHM_(x)=0.8 degrees) and a full-width half-maximumangle of diffusion in a vertical y direction of 3.75 degrees(FWHM_(y)=3.75 degrees). This configuration beneficially spreads thelight in the vertical direction which can be useful for situations inwhich it is desirable to limit the horizontal spread of the light, e.g.light sent back for viewing by just one person, but allows for multiplevertical viewing positions, e.g. accommodating viewers with differingheights. The superimposed rectangular region shown in FIG. 4 representsa desired viewing region which is serviced by the combination ofretroreflective film and diffusing film.

In some cases, the use of a diffusing film as a beam broadeningtechnique can be combined with the aforementioned modification ofdihedral angle errors to produce an optimal profile for a givenapplication. Alternatively, each technique can be employed separately.

The dihedral angle technique can be advantageous, for example, if it isdesired for the transitions from bright to dark to be fairly abrupt.This technique can, though, require tooling for each new design in aprocess that can be costly and time-consuming.

The diffusing film technique can be advantageous, for example, if it isdesired to hide seams in the prismatic film. Different diffusing filmscan also be matched with different prismatic films to accommodate theneeds of various applications with increased flexibility. This techniquecan, though, add cost to the display screen, and produce light intensityor brightness transitions that are less abrupt.

As described above, the adjustment of the dihedral angles of the cubecorner prism retroreflective elements can also influence the shapes ofthe reflected light beams returned by the retroreflective article.Through the selection of particular dihedral angle combinations, thesize of the viewing regions or patches can be increased as desired,while maintaining sufficient uniformity of illumination within eachpatch and among the two patches. In some of these embodiments, theretroreflective film is used in conjunction with a diffusing film, whichcan help to reduce the visibility of seam lines and to improve in screenuniformity. This use of the diffusing film and the control of thedihedral angles also can increase the size of the patch and help withuniformity within the patch. Accordingly, the design of the prisms canbe configured to provide for a smaller patch if used with a strongerdiffuser, or a larger patch if used with a weaker diffuser or nodiffuser. Likewise, if the retroreflective film design provides a largerpatch, a weaker diffuser or no diffuser can be selected. Alternatively,if the retroreflective film provides a smaller patch, a strongerdiffuser can be selected. The width and height of the patches can becontrolled independently, either by using anisotropic diffusers, or byvarying the dihedral angle pattern to affect the aspect ratio of thepatch. Combinations of these approaches can provide more flexibility.

The configurations of the retroreflective elements disposed on the backsurface of the retroreflective film can be determined by geometries ofsets of substantially parallel grooves in the back surface, wherein thesets determine the positioning of the retroreflective elements. Theconfigurations and arrangements of these groove sets can thereforedetermine the cube cant, prism depth, and/or dihedral angle errors ofprism retroreflective elements. As used herein, the term “substantiallyparallel grooves” refers to grooves that are substantially parallel toone another, e.g. parallel to one another. Each of the grooves has agroove axis extending along the length of the groove, wherein the anglebetween the groove axes of two substantially parallel grooves has amagnitude less than 5 degrees, e.g., less than 4 degrees, less than 3degrees, less than 2 degrees, or less than 1 degree. The respectivegrooves may differ from one another in slope by a magnitude less than 5degrees, e.g., less than 4 degrees, less than 3 degrees, less than 2degrees, or less than 1 degree, when compared to the slope of a basisline.

Illustrative examples of the groove sets are shown in FIGS. 5A-5D, whichprovide an overview of a cutting process used to produce theretroreflective elements. In FIG. 5A, a first set of substantiallyparallel grooves is shown cut into a substrate of which a replica or acast can be used to emboss the retroreflective film back surface. Thegrooves can be cut using a cutting tool having a pointed tip. In someembodiments, the cutting tool tip also includes a flat region, such thata flat region is created in the substrate between adjacentretroreflective elements. The presence of such flat regions can boosttransparency, but at the cost of efficiency. Each groove is cut along agroove axis, and typically has a v shape with two intersecting groovesides. The grooves of this first set have half angles “a” and “b” thatare defined by corresponding “a” and “b” angles on the surface of theshown cutting tool. The half angles are formed between the groove sidesand a plane parallel to the groove axis and perpendicular to the planeof the substrate or the back surface of the retroreflective film. Thesizes and tilts of the cutting tool, grooves, and retroreflectiveelements have been exaggerated in this and the following figures forclarity. In some embodiments, each groove of the first set is separatedfrom the adjacent groove of the set by a substantially identicalspacing, e.g., a first spacing. The first spacing can, for example,range from 0.03 mm to 0.27 mm, e.g., from 0.03 mm to 0.15 mm, from 0.06mm to 0.18 mm, from 0.09 mm to 0.21 mm, from 0.12 mm to 0.24 mm, or from0.15 mm to 0.27 mm. The first spacing can range from 0.1 mm to 0.2 mm,e.g., from 0.1 to 0.16 mm, from 0.11 mm to 0.17 mm, from 0.12 mm to 0.18mm, from 0.13 mm to 0.19 mm, or from 0.14 mm to 0.2 mm. In terms ofupper limits, the first spacing can be greater than 0.03 mm, e.g.,greater than 0.06 mm, greater than 0.09 mm, greater than 0.12 mm,greater than 0.15 mm, greater than 0.18 mm, greater than 0.21 mm, orgreater than 0.24 mm. In terms of lower limits, the first spacing can beless than 0.27 mm, e.g., less than 0.24 mm, less than 0.21 mm, less than0.18 mm, less than 0.15 mm, less than 0.12 mm, less than 0.09 mm, orless than 0.06 mm.

In FIG. 5B, a second set of substantially parallel grooves is shown cutinto the substrate along with the first groove set. Similarly to thefirst set grooves, the grooves of this second set can have half angles“a” and “b” that are defined by corresponding “a” and “b” angles on thesurface of the same cutting tool used to produce the first set grooves.In some embodiments, each groove of the second set is separated from theadjacent groove of the set by a substantially identical spacing (i.e., asecond spacing). The second spacing can be, for example, range from 0.03mm to 0.27 mm, e.g., from 0.03 mm to 0.15 mm, from 0.06 mm to 0.18 mm,from 0.09 mm to 0.21 mm, from 0.12 mm to 0.24 mm, or from 0.15 mm to0.27 mm. The second spacing can range from 0.1 mm to 0.2 mm, e.g., from0.1 to 0.16 mm, from 0.11 mm to 0.17 mm, from 0.12 mm to 0.18 mm, from0.13 mm to 0.19 mm, or from 0.14 mm to 0.2 mm. In terms of upper limits,the second spacing can be greater than 0.03 mm, greater than 0.06 mm,greater than 0.09 mm, greater than 0.12 mm, greater than 0.15 mm,greater than 0.18 mm, greater than 0.21 mm, or greater than 0.24 mm. Interms of lower limits, the second spacing can be less than 0.27 mm, lessthan 0.24 mm, less than 0.21 mm, less than 0.18 mm, less than 0.15 mm,less than 0.12 mm, less than 0.09 mm, or less than 0.06 mm.

In some embodiments, and as shown in FIGS. 5A-5D, the grooves of thefirst set have a spacing substantially identical to that of the groovesof the second set. As used herein, the term “spacing substantiallyidentical” refers to a relationship between two spacings wherein thespacings are within 20% of one another. For example, two spacings have aspacing substantially identical to one another if the spacings arewithin 18%, within 16%, within 14%, within 12%, within 10%, within 9%,within 8%, within 7%, within 6%, within 5%, within 4%, within 3%, within2%, or within 1% of one another.

In FIG. 5C, a third set of substantially parallel grooves is shown cutinto the substrate along with the first and second groove sets. Thegrooves of this third set have half angles “c” and “d” that are definedby corresponding “c” and “d” angles on the surface of the shown cuttingtool. In some embodiments, each groove of the third set is separatedfrom the adjacent groove of the set by a substantially identical spacing(i.e., a third spacing). The third spacing can be, for example, rangefrom 0.03 mm to 0.27 mm, e.g., from 0.03 mm to 0.15 mm, from 0.06 mm to0.18 mm, from 0.09 mm to 0.21 mm, from 0.12 mm to 0.24 mm, or from 0.15mm to 0.27 mm. The third spacing can range from 0.1 mm to 0.2 mm, e.g.,from 0.1 to 0.16 mm, from 0.11 mm to 0.17 mm, from 0.12 mm to 0.18 mm,from 0.13 mm to 0.19 mm, or from 0.14 mm to 0.2 mm. In terms of upperlimits, the third spacing can be greater than 0.03 mm, greater than 0.06mm, greater than 0.09 mm, greater than 0.12 mm, greater than 0.15 mm,greater than 0.18 mm, greater than 0.21 mm, or greater than 0.24 mm. Interms of lower limits, the third spacing can be less than 0.27 mm, lessthan 0.24 mm, less than 0.21 mm, less than 0.18 mm, less than 0.15 mm,less than 0.12 mm, less than 0.09 mm, or less than 0.06 mm. In someembodiments, the grooves of the third set have a spacing smaller thanthe first and second spacing. In some embodiments, the grooves of thethird set have a spacing larger than the first and second spacing.

FIG. 5D is a plan view of an array of cube corner prisms bounded by thefirst, second, and third grooves in the back surface of aretroreflective film in accordance with an embodiment. The illustrationshows the array of cube corner prisms bounded by the three sets ofsubstantially parallel grooves. The particular geometry of an individualcube corner element of the array will depend on the particular halfgrooves of the element border. For example, a cube corner element can bebounded by an “a” half groove from a first set groove, an “a” halfgroove from a second set groove, and a “c” half groove from a third setgroove. In this case, the cube corner can be considered an “aac”element. Similarly, with the grooves as shown in FIGS. 5A-5D, cubecorners can alternatively be “aad”, “abc”, “abd”, “bac”, “bad”, “bbd”,or “bbc” elements.

In some embodiments, one or both of the half angles of the third groovesranges from 25 degrees to 28.5 degrees, e.g., from 25 degrees to 26.9degrees, from 25.4 degrees to 27.3 degrees, from 25.8 degrees to 27.7degrees, from 26.2 degrees to 28.1 degrees, or from 26.6 degrees to 28.5degrees. One or both of the third groove half angles can range from 43.5degrees to 45 degrees, e.g., from 43.5 degrees to 44.2 degrees, from43.7 degrees to 44.4 degrees, from 43.9 degrees to 44.6 degrees, from44.1 degrees to 44.8 degrees, or from 44.3 degrees to 45 degrees. Interms of lower limits, one or both of the third groove half angles canbe greater than 25 degrees, e.g., greater than 25.4 degrees, greaterthan 25.8 degrees, greater than 26.2 degrees, greater than 26.6 degrees,greater than 26.9 degrees, greater than 27.3 degrees, greater than 27.7degrees, greater than 28.1 degrees, greater than 43.5 degrees, greaterthan 43.7 degrees, greater than 43.9 degrees, greater than 44.1 degrees,greater than 44.3 degrees, greater than 44.4 degrees, greater than 44.6degrees, or greater than 44.8 degrees. In terms of upper limits, one orboth of the third groove half angles can be less than 45 degrees, e.g.,less than 44.8 degrees, less than 44.6 degrees, less than 44.4 degrees,less than 44.2 degrees, less than 44.1 degrees, less than 43.9 degrees,less than 43.7 degrees, less than 28.5 degrees, less than 28.1 degrees,less than 27.7 degrees, less than 27.3 degrees, less than 26.9 degrees,less than 26.6 degrees, less than 26.2 degrees, less than 25.8 degrees,or less than 25.4 degrees.

The depth of the grooves gives each of the cube corner prisms of thearray a cube corner depth. The cube corner depth is defined as thedistance between the maximum height of the cube corner prism and thebase of the cube corner prism. The cube corner depth can, for example,range from 1 mil to 5 mils, e.g., from 1 mil to 3.4 mils, from 1.4 milsto 3.8 mils, from 1.8 mils to 4.2 mils, from 2.2 mils to 4.6 mils, orfrom 2.6 mils to 5 mils. The cube corner depth can range from 2.2 milsto 3.8 mils, e.g., from 2.2 mils to 3 mils, from 2.4 mils to 3.2 mils,from 2.6 mils to 3.4 mils, from 2.8 mils to 3.6 mils, or from 3 mils to3.8 mils. In terms of lower limits, the cube corner depth can be greaterthan 1 mil, e.g., greater than 1.4 mils, greater than 1.8 mils, greaterthan 2.2 mils, greater than 2.6 mils, greater than 3 mils, greater than3.4 mils, greater than 3.8 mils, greater than 4.2 mils, or greater than4.6 mils. In terms of upper limits, the cube corner depth can be lessthan 5 mils, e.g., less than 4.6 mils, less than 4.2 mils, less than 3.8mils, less than 3.4 mils, less than 3 mils, less than 2.6 mils, lessthan 2.2 mils, less than 1.8 mils, or less than 1.4 mils.

In this discussion, we define cant as the cant of the unaberrated cubehaving the same cube shape, and we also consider the third groove halfangle (HG₃). This angle has functional relevance for transparencyeffects, and also for the horizontal entrance angularity. As is shown inthe graph of FIG. 6, for the case of a 6-degree offset with normalincidence of light, prism designs that use a negative value of e₃ arealways more efficient in returning light, with a value of HG₃ ofapproximately 35 degrees giving the highest efficiency.

In some embodiments, the cube corner prisms of the retroreflectivearticle are canted face-more-parallel, e.g., at a cant ranging from −3degrees to −10 degrees. The cube corner prisms can have a cant rangingfrom −3 degrees to −8 degrees, from −3.5 degrees to −8.5 degrees, from−4 degrees to −9 degrees, from −4.5 degrees to −9.5 degrees, or from −5degrees to −10 degrees. The cant can range from −5 degrees to −8degrees, e.g., from −5 degrees to −6.8 degrees, from −5.3 degrees to−7.1 degrees, from −5.6 degrees to −7.4 degrees, from −5.9 degrees to−7.7 degrees, or from −6.2 degrees to −8 degrees. In terms of lowerlimits, the cant can be greater than −10 degrees, e.g., greater than−9.5 degrees, greater than −9 degrees, greater than −8.5 degrees,greater than −8 degrees, greater than −7.5 degrees, greater than −7degrees, greater than −6.5 degrees, greater than −6 degrees, greaterthan −5.5 degrees, greater than −5 degrees, greater than −4.5 degrees,greater than −4 degrees, or greater than −3.5 degrees. In terms of upperlimits, the cant can be less than −3 degrees, e.g., less than −3.5degrees, less than −4 degrees, less than −4.5 degrees, less than −5degrees, less than −5.5 degrees, less than −6 degrees, less than −6.5degrees, less than −7 degrees, less than −7.5 degrees, less than −8degrees, less than −8.5 degrees, less than −9 degrees, or less than −9.5degrees.

In some embodiments, the cube corner prisms of the retroreflectivearticle are canted edge-more-parallel, e.g., at a cant ranging from 3degrees to 10 degrees. The cube corner prisms can have a cant rangingfrom 3 degrees to 8 degrees, from 3.5 degrees to 8.5 degrees, from 4degrees to 9 degrees, from 4.5 degrees to 9.5 degrees, or from 5 degreesto 10 degrees. The cant can range from 5 degrees to 8 degrees, e.g.,from 5 degrees to 6.8 degrees, from 5.3 degrees to 7.1 degrees, from 5.6degrees to 7.4 degrees, from 5.9 degrees to 7.7 degrees, or from 6.2degrees to 8 degrees. In terms of upper limits, the cant can be lessthan 10 degrees, less than 9.5 degrees, less than 9 degrees, less than8.5 degrees, less than 8 degrees, less than 7.5 degrees, less than 7degrees, less than 6.5 degrees, less than 6 degrees, less than 5.5degrees, less than 5 degrees, less than 4.5 degrees, less than 4degrees, or less than 3.5 degrees. In terms of lower limits, the cantcan be greater than 3 degrees, e.g., greater than 3.5 degrees, greaterthan 4 degrees, greater than 4.5 degrees, greater than 5 degrees,greater than 5.5 degrees, greater than 6 degrees, greater than 6.5degrees, greater than 7 degrees, greater than 7.5 degrees, greater than8 degrees, greater than 8.5 degrees, greater than 9 degrees, or greaterthan 9.5 degrees.

The terms “canted face-more-parallel” and “canted edge-more parallel” asused herein refer to the positioning of the cube relative to theprincipal refracted ray. When the angles between the cube faces and theprincipal refracted ray are not all equal to 35.26 degrees, the cube is“face-more-parallel” or “edge-more-parallel” depending upon whether theface angle with respect to the principal refracted ray that is mostdifferent from 35.26 degrees is respectively greater or less than 35.26degrees. In the case of sheeting or other retroreflectors for which theprincipal refracted ray is nominally perpendicular to the front surfaceof the retroreflector, then for face-more-parallel cubes the selectedcube face will also be more parallel to the reflector front surface thanwill any face of an uncanted cube.

The data presented in FIG. 6 suggest that in some instances, a thirdgroove half angle of 35 degrees would be preferred since thisconfiguration can give the highest retroreflective efficiency. However,in a display application the head-on efficiency is commonly not the onlyproperty of interest. Rather, it is often desirable for a display tohave a retroreflective efficiency that is not only high, but also iswell maintained for all light entrance angles of the display.

The plots of FIG. 7 show the retroreflective efficiency (R_(T)), as afunction of horizontal entrance angle (β_(x)) and vertical entranceangle (β_(y)) for five values of the third groove half angle (HG₃=25degrees, 30 degrees, 35 degrees, 40 degrees, and 45 degrees). The rangeof values for β_(x) and β_(y) shown are typical for projection screens.The positions of angle combinations (β_(x), β_(y)) shown on the graphroughly correspond topologically to (x, y) positions on a flat displayscreen with the projector located opposite the top center of the screen.The efficiency value R_(T) at each position then is one factor indetermining the brightness of the corresponding x,y position on thescreen.

As expected, the efficiency values shown in FIG. 7 tend to be higher forHG₃=35 degrees and fall off at higher or lower half angle values.However, although the head-on efficiency is higher when HG₃=35 degrees,there are regions at the edge of the screen that are very dark(R_(T)<5%). For HG₃=30 degrees or 40 degrees the uniformity ofretroreflective efficiency improves, although there still are some darkregions (R_(T)<10%). For HG₃=25 degrees or 45 degrees, the efficiencyuniformity improves further, such that for all regions on the screenR_(T)>15%. Other factors can also affect screen uniformity, but based onthis estimated analysis it can be preferable to have a third groove halfangle within the range between 25 degrees and 28.5 degrees, or withinthe range between 43.5 degrees and 45.0 degrees. These third groove halfangle values correspond to cube corner prisms having a sizable negativeor positive cant.

FIG. 8 presents a graph plotting the retroreflective efficiency as afunction of the horizontal entrance angle (β_(x)) for five differentthird groove half angle values (25 degrees, 30 degrees, 35 degrees, 40degrees, and 45 degrees). The trends represent profiles from along thetops of the graphs of FIG. 7. From FIG. 8 it can be seen that there areangles for which the efficiency drops off to a lower level. Theseinstances of rapid efficiency decline can also be seen on the contourgraphs of FIG. 7. As discussed above, although the case of HG₃=35degrees has the highest efficiency at β_(x)=0 degrees, the efficiencyvalues of this trend drop off dramatically at β_(x)=−20 degrees and 20degrees. This indicates that if a projection scenario involves β_(x)values less than −20 degrees or greater than 20 degrees, as can often bethe case, there is a potential for non-uniformity in the perceivedbrightness of the screen. For the trend line associated with HG₃=25degrees, the overall efficiency also begins to drop, which can be apotential disadvantage. The HG₃ values between 25 degrees and 30 degreeshave the greatest absence of very dark areas, as well as the least rapidefficiency declines. It is also notable that one of the preferred HG₃ranges of between 43.5 degrees and 45 degrees can also have issues withuniformity. For example, for the case of HG₃=45 degrees, the efficiencydrops dramatically at β_(x)=−5 degrees and 5 degrees. However, at valuesbeyond these, the loss of efficiency corresponds to an increase invisual transparency, which can be a significant advantage for functionaland aesthetic reasons.

Another advantage for this third groove half angle range between 43.5degrees and 45 degrees is that it can provide superior horizontalpattern stability. Changes in β_(x) and β_(y) can move the pattern ofretroreflected light horizontally. However, in the case of an HG₃ valuein the range between 43.5 degrees and 45 degrees, changes due to β_(x)tend to compensate for changes in β_(y), resulting in the patternstaying more stable in the horizontal direction.

FIG. 9A shows a plot of the position of a light beam returned by aretroreflective article having an offset of 6 degrees, a third groovehalf angle of 29.5 degrees, and a diffusing film. The plot also shows aviewing zone superimposed on the light beam position for the case ofhead-on viewing (β_(x)=0 degrees, β_(y)=0 degrees). If the viewerinstead looks obliquely toward the lower right of the screen (β_(x)=20degrees, β_(y)=−15 degrees), the pattern of light return shifts bothhorizontally and vertically as shown in FIG. 9B. The vertical shift tothe light position is inconsequential since the desired viewing regionalso shifts vertically. However, the horizontal shift causes the lightreturn to decrease substantially, particularly in the left portion ofthe desired viewing region.

If instead the prism cant is changed such that the third groove halfangle is 44.4 degrees, then the light return for head on viewing is asshown on FIG. 10A. In this case, if the viewer instead looks obliquelytoward the lower right of the screen (β_(x)=20 degrees, β_(y)=−15degrees), the pattern of light return again shifts both horizontally andvertically as shown in FIG. 10B. The vertical downward shift of thepattern of light can be undesirable, but has a reduced negative effectsince the pattern of light has a substantial vertical spread. Byshifting the desired viewing region downward (e.g., by raising theprojector), this vertical shift can be easily accommodated. Importantly,the horizontal shift in this case is significantly less than that ofFIG. 9B, and can also be accommodated.

In some applications, it is desirable to have the viewer positioned notdirectly above or below the projector, but instead offset from theprojector in a direction either towards or farther away from theretroreflective article. This forward or backward offset introduces ahorizontal instability in the desired viewing area due to parallax. Insuch cases, an appropriately designed retroreflective article cancompensate for the horizontal instability by providing an appropriateamount of horizontal pattern shift.

FIG. 11A shows a plot of the position of a light beam returned by theretroreflective article and diffusing film of FIG. 9A superimposed witha viewing zone for head-on viewing offset 0.3 m in a direction away fromboth the projector and the retroreflective article, e.g., offset 0.3 mbehind the projector. From this offset viewing position, if the viewerlooks obliquely toward the lower right of the screen (β_(x)=20 degrees,β_(y)=−15 degrees), the pattern of light return again shifts bothhorizontally and vertically as shown in FIG. 11B, but the horizontalshift has now been matched by the horizontal shift in the viewing area,reducing the undesired decrease in light return depicted in FIG. 9B withthe same retroreflective article configuration.

An additional advantageous outcome of this small half-angle design(e.g., a configuration having an HG₃ value between 25 degrees and 30degrees) is that the overall brightness uniformity of the screen imagecan be considerably improved, as is shown in FIG. 12. The left image ofFIG. 12 is a top-down illustration of viewing a retroreflective articlehaving an HG₃ value in the range from 40 degrees to 45 degrees from aposition offset behind a projector and farther away from theretroreflective article. In this case, the right eye of the viewer is ina position far to the right of the return path of light reflecting backfrom the right side of the retroreflective article, while the left eyeof the viewer is in a position far to the left of the return path oflight reflecting back from the left side of the retroreflective article.This results in a reduction in effective brightness at the edges of theretroreflective article, and can also cause a significant difference inthe levels of brightness perceived by the left and right eyes for theedges of the retroreflective article, which can cause viewer discomfort.The right image of FIG. 12 is a top-down illustration of viewing a smallhalf-angle retroreflective article having an HG₃ value in the range of25 degrees to 30 degrees from the offset position. In this case, allregions of the retroreflective article reflect to the general proximityof the center of the eyes, improving both brightness uniformity andperceived left and right eye brightness balance for the viewer.

The HG₃ value for the small half-angle retroreflective article can, forexample, range from 25 degrees to 30 degrees, e.g., from 25 degrees to28 degrees, from 25.5 degrees to 28.5 degrees, from 26 degrees to 29degrees, from 26.5 degrees to 29.5 degrees, or from 27 degrees to 30degrees. In terms of upper limits, the HG₃ value can be less than 30degrees, e.g., less than 29.5 degrees, less than 29 degrees, less than28.5 degrees, less than 28 degrees, less than 27.5 degrees, less than 27degrees, less than 26.5 degrees, less than 26 degrees, or less than 25.5degrees. In terms of lower limits, the HG₃ value can be greater than 25degrees, e.g., greater than 25.5 degrees, greater than 26 degrees,greater than 26.5 degrees, greater than 27 degrees, greater than 28degrees, greater than 29 degrees, or greater than 29.5 degrees. At lowervalues of HG₃, the efficiency of the retroreflective article can bereduced, resulting in lower overall brightness. Also, at lower values ofHG₃ certain characteristic perceived brightness instabilities can occurat sufficiently low values of β_(x) (e.g., lower than 45 degrees), ascan occur in certain screen projection scenarios. These undesirableinstabilities can appear as sparkles, bright lines, or streaks on theretroreflective article or screen. Conversely, at higher values of HG₃,the performance of the retroreflective article at larger entrance anglesis diminished, and there can be a consequent lowering of the brightnessat the edge of the retroreflective article.

In some embodiments, the retroreflective elements of the smallhalf-angle retroreflective article are not produced using the techniqueof tilting the cutting tool to produce pattern spread. Instead, it canbe more beneficial for certain applications to configure theretroreflective article to produce narrow reflected beams, and to obtaina desired pattern spread by the alternate means of a diffusing film. Inthis case, a stronger diffuser can be used, providing the additionalbenefits of effectively minimizing front surface specular reflection andhiding seams and other cosmetic defects.

The diffusing film used with the small half-angle retroreflectivearticle can have a full-width half-maximum angle of diffusion in ahorizontal x-direction ranging, for example, from 1 degree to 4 degrees,e.g., from 1 degree to 2.8 degrees, from 1.3 degrees to 3.1 degrees,from 1.6 degrees to 3.4 degrees, from 1.9 degrees to 3.7 degrees, orfrom 2.2 degrees to 4 degrees. In terms of upper limits, the horizontalx-direction diffusion angle of the diffuser can be less than 4 degrees,e.g., less than 3.7 degrees, less than 3.4 degrees, less than 3.1degrees, less than 2.8 degrees, less than 2.5 degrees, less than 2.2degrees, less than 1.9 degrees, less than 1.6 degrees, or less than 1.3degrees. In terms of lower limits, the horizontal x-direction diffusionangle of the diffuser can be greater than 1 degree, e.g., greater than1.3 degrees, greater than 1.6 degrees, greater than 1.9 degrees, greaterthan 2.2 degrees, greater than 2.5 degrees, greater than 2.8 degrees,greater than 3.1 degrees, greater than 3.4 degrees, or greater than 3.7degrees. Larger horizontal diffusion angles, e.g., greater than 4degrees, and smaller horizontal diffusion angles, e.g., less than 1degree, are also contemplated.

The diffusing film used with the small half-angle retroreflectivearticle can have a full-width half-maximum angle of diffusion in avertical y-direction ranging, for example, from 3 degrees to 6 degrees,e.g., from 3 degrees to 4.8 degrees, from 3.3 degrees to 5.1 degrees,from 3.6 degrees to 5.4 degrees, from 3.9 degrees to 5.7 degrees, orfrom 4.2 degrees to 6 degrees. In terms of upper limits, the verticaly-direction diffusion angle of the diffuser can be less than 6 degrees,e.g., less than 5.7 degrees, less than 5.4 degrees, less than 5.1degrees, less than 4.8 degrees, less than 4.5 degrees, less than 4.2degrees, less than 3.9 degrees, less than 3.6 degrees, or less than 3.3degrees. In terms of lower limits, the vertical y-direction diffusionangle of the diffuser can be greater than 3 degrees, e.g., greater than3.3 degrees, greater than 3.6 degrees, greater than 3.9 degrees, greaterthan 4.2 degrees, greater than 4.5 degrees, greater than 4.8 degrees,greater than 5.1 degrees, greater than 5.4 degrees, or greater than 5.7degrees. Larger vertical diffusion angles, e.g., greater than 6 degrees,and smaller vertical diffusion angles, e.g., less than 3 degrees, arealso contemplated.

In certain aspects, the prisms of the small half-angle retroreflectivearticle have a third dihedral angle error that has a magnitude greaterthan 1 degrees. The third dihedral angle error can, for example, rangefrom −4 degrees to −1 degrees, e.g., from −4 degrees to −2.2 degrees,from −3.7 degrees to −1.9 degrees, from −3.4 degrees to −1.6 degrees,from −3.1 degrees to −1.3 degrees, or from −2.8 degrees to −1 degrees.In terms of upper limits, the third dihedral angle error can be lessthan −1 degrees, e.g., less than −1.3 degrees, less than −1.6 degrees,less than −1.9 degrees, less than −2.2 degrees, less than −2.5 degrees.less than −2.8 degrees, less than −3.1 degrees, less than −3.4 degrees,or less than −3.7 degrees. In terms of upper limits, the third angledihedral angle error can be greater than −4 degrees. e.g., greater than−3.7 degrees, greater than −3.4 degrees, greater than −3.1 degrees,greater than −2.8 degrees, greater than −2.5 degrees, greater than −2.2degrees, greater than −1.9 degrees, greater than −1.6 degrees, orgreater than −1.3 degrees. Larger third dihedral angle errors, e.g.,greater than −1 degrees, and smaller dihedral angle errors, e.g., lessthan −4 degrees, are also contemplated.

The third dihedral angle error can, for example, range from 1 degree to4 degrees, e.g., from 1 degree to 2.8 degrees, from 1.3 degrees to 3.1degrees, from 1.6 degrees to 3.4 degrees, from 1.9 degrees to 3.7degrees, or from 2.2 degrees to 4 degrees. In terms of upper limits, thethird dihedral angle error can be less than 4 degrees, e.g., less than3.7 degrees, less than 3.4 degrees, less than 3.1 degrees, less than 2.8degrees, less than 2.5 degrees, less than 2.2 degrees, less than 1.9degrees, less than 1.6 degrees, or less than 1.3 degrees. In terms oflower limits, the third dihedral angle error can be greater than 1degree, e.g., greater than 1.3 degrees, greater than 1.6 degrees,greater than 1.9 degrees, greater than 2.2 degrees, greater than 2.5degrees, greater than 2.8 degrees, greater than 3.1 degrees, greaterthan 3.4 degrees, or greater than 3.7 degrees. Larger dihedral angleerrors, e.g., greater than 4 degrees, and smaller dihedral angle errors,e.g., less than 1 degree, are also contemplated. In certain aspects, thefirst and second dihedral angle errors of the prisms of theretroreflective article are each 0 degrees.

In some embodiments, the prisms of the small half-angle retroreflectivearticle are each canted edge-more-parallel at a cant greater than 0degrees. The cant of each prism can, for example, range from 0 degreesto 10 degrees, e.g., from 0 degrees to 6 degrees, from 1 degree to 7degree, from 2 degrees to 8 degrees, from 3 degrees to 9 degrees, orfrom 4 degrees to 10 degrees. In terms of upper limits, the cant of eachprism can be less than 10 degrees, e.g., less than 9 degrees, less than8 degrees, less than 7 degrees, less than 6 degrees, less than 5degrees, less than 4 degrees, less than 3 degrees, less than 2 degrees,or less than 1 degree. In terms of lower limits, the cant of each prismcan be greater than 0 degrees, e.g., greater than 1 degree, greater than2 degrees, greater than 3 degrees, greater than 4 degrees, greater than5 degrees, greater than 6 degrees, greater than 7 degrees, greater than8 degrees, or greater than 9 degrees. Larger prism cants, e.g., greaterthan 10 degrees, are also contemplated.

The present disclosure also relates to a display system that includesthe retroreflective article as described above. The system also includesa light source that produces the incident light beam at least in thedirection of the retroreflective article. In a preferred embodiment, thelight source is a projector configured to direct an incident light beamtowards the retroreflective article. The incident light can be, forexample, a still image or a video image. In some embodiments, the systemincludes two or more light sources or projectors. Each of the one ormore projectors can include one or more optical elements for directingand/or focusing an image or video onto the retroreflective article.Projectors can include, for example and without limitation, filmprojectors, cathode ray tube (CRT) projectors, laser projectors, DigitalLight Processor (DLP) or Digital Micromirror Device (DMD) projectors,liquid crystal display (LCD) projectors, or liquid crystal on silicon(LCOS) projectors.

The system can also include a computer processor operatively connectedwith a machine-readable non-transitory storage medium. Storage media caninclude any or all of the tangible memory of the computers, processorsor the like, or associated modules thereof, such as varioussemiconductor memories, tape drives, disk drives and the like, which canprovide non-transitory storage at any time for software programming. Allor portions of the software can at times be communicated through theInternet or various other telecommunication networks. Suchcommunications, for example, can enable loading of the software from onecomputer or processor into another, for example, from a managementserver or host computer into the computer platform of an applicationserver. Thus, another type of media that can bear the software elementsincludes optical, electrical, and electromagnetic waves, such as usedacross physical interfaces between local devices, through wired andoptical landline networks, and over various air-links. The physicalelements that carry such waves, such as wired or wireless links, opticallinks or the like, also can be considered as media bearing the software.Through the software, for example, the storage medium can embodyinformation indicative of instructions for causing the processor toperform operations. The operations can include, for example, controllingthe light source or projector to direct the incident light beam towardsthe retroreflective article.

The following embodiments are contemplated. All combinations of featuresand embodiment are contemplated.

Embodiment 1: A retroreflective article comprising: a retroreflectivefilm comprising opposing front and back surfaces; and a plurality ofretroreflective elements disposed on the back surface of theretroreflective film; wherein each of the retroreflective elementscomprises a non-equilateral triangular pyramid prism bounded by one of afirst set of substantially parallel and v-shaped first grooves, one of asecond set of substantially parallel and v-shaped second grooves, andone of a third set of substantially parallel and v-shaped third grooves;wherein each of the grooves comprises a groove axis and two intersectinggroove sides; wherein each groove side of a groove forms a half anglebetween the groove side and a plane parallel to the groove axis of thegroove and orthogonal to the back surface of the retroreflective film;and wherein at least one of the half angles ranges from 25.0 degrees to28.5 degrees, or ranges from 43.5 degrees to 45.0 degrees.

Embodiment 2: An embodiment of embodiment 1, wherein at least one of thehalf angles ranges from 25.0 degrees to 28.5 degrees.

Embodiment 3: An embodiment of embodiment 1, wherein at least one of thehalf angles ranges from 43.5 degrees to 45.0 degrees.

Embodiment 4: An embodiment of any embodiment of embodiments 1-3,wherein each of the retroreflective elements comprises a first, second,and third triangular face; wherein the first, second, and thirdtriangular faces intersect at an apex configured to point away from theback surface; wherein the first and second triangular faces aresubstantially congruent triangles; and wherein the third triangular faceis not congruent with the first and second triangular faces.

Embodiment 5: An embodiment of any embodiment of embodiments 1-4,wherein each prism has a first, second, and third dihedral angle error;and wherein the magnitude of each dihedral angle error ranges from 0.01degrees to 10 degrees.

Embodiment 6: An embodiment of embodiment 5, wherein the magnitude ofeach dihedral angle error ranges from 0.01 degrees to 4 degrees.

Embodiment 7: An embodiment of embodiment 5 or 6, wherein the magnitudeof each third dihedral angle error is greater than 1 degree.

Embodiment 8: An embodiment of any embodiment of embodiments 5-7,wherein the magnitude of the average of the first dihedral angle errorsis less than 0.3 degrees, wherein the magnitude of the average of thesecond dihedral errors is less than 0.3 degrees, and wherein the averageof the third dihedral angle errors is less than −1 degrees.

Embodiment 9: An embodiment of any embodiment of embodiments 1-8,wherein adjacent first grooves are separated by a first spacing rangingfrom 0.1 mm to 0.2 mm; wherein adjacent second grooves are separated bya second spacing substantially identical to the first spacing; andwherein adjacent third grooves are separated by a third spacing smallerthan the first and second spacing.

Embodiment 10: An embodiment of any embodiment of embodiments 1-9,wherein the depth of each prism ranges from 1 mil to 5 mils.

Embodiment 11: An embodiment of any embodiment of embodiments 1-10,wherein the each prism is canted face-more-parallel.

Embodiment 12: An embodiment of embodiment 11, wherein each prism iscanted at a cant angle ranging from −5 degrees to −8 degrees.

Embodiment 13: An embodiment of any embodiment of embodiments 1-10,wherein each prism is canted edge-more-parallel.

Embodiment 14: An embodiment of embodiment 13, wherein each prism iscanted at a cant angle ranging from 4 degrees to 8 degrees.

Embodiment 15: An embodiment of any embodiment of embodiments 1-14,further comprising: a diffusing film having a full-width half-maximumangle of diffusion of less than 1 degree in a horizontal x directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.

Embodiment 16: An embodiment of any embodiment of embodiments 1-14,further comprising: a diffusing film having a full-width half-maximumangle of diffusion of greater than 3 degrees in a vertical y directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.

Embodiment 17: An embodiment of any embodiment of embodiments 1-14,further comprising: a diffusing film having: (1) a full-widthhalf-maximum angle of diffusion of less than 1 degree in a horizontalx-direction substantially parallel to the front surface of theretroreflective film when the front and back surfaces of theretroreflective film are positioned vertically, and (2) a full-widthhalf-maximum angle of diffusion of greater than 3 degrees in a verticaly-direction substantially parallel to the front surface of theretroreflective film when the front and back surfaces of theretroreflective film are positioned vertically.

Embodiment 18: An embodiment of any embodiment of embodiments 15-17,wherein the diffusing film is directly adjacent to the front surface ofthe retroreflective film.

Embodiment 19: An embodiment of any embodiment of embodiments 1-18,wherein the retroreflective film comprises acrylic or polycarbonate.

Embodiment 20: An embodiment of any embodiment of embodiments 1-19,wherein each of the retroreflective elements are air-backed.

Embodiment 21: An embodiment of any embodiment of embodiments 1-20,wherein the retroreflective article is a display screen.

Embodiment 22: A retroreflective article comprising: a retroreflectivefilm comprising opposing front and back surfaces; and a plurality ofretroreflective elements disposed on the back surface of theretroreflective film; wherein each of the retroreflective elements is anon-equilateral triangular pyramid prism comprising a triangular base;and wherein the triangular base comprises two sides that differ inlength from one another such that the ratio of the length of the smallerof the two sides to the length of the larger of the two sides rangesfrom 80% to 92.5%.

Embodiment 23: An embodiment of embodiment 22, wherein the ratio of thelength of the smaller of the two sides to the length of the larger ofthe two sides ranges from 83% to 90% .

Embodiment 24: An embodiment of embodiment 22 or 23, wherein eachretroreflective element further comprises a first, second, and thirdtriangular face; wherein the first, second, and third triangular facesintersect at an apex configured to point away from the back surface;wherein the first and second triangular faces are substantiallycongruent triangles; and wherein the third triangular face is notcongruent with the first and second triangular faces.

Embodiment 25: An embodiment of any embodiment of embodiments 22-24,wherein each prism has a first, second, and third dihedral angle error;and wherein the magnitude of each dihedral angle error ranges from 0.01degrees to 10 degrees.

Embodiment 26: An embodiment of embodiment 25, wherein the magnitude ofeach dihedral angle error ranges from 0.01 degrees to 4 degrees.

Embodiment 27: An embodiment of embodiment 25 or 26, wherein themagnitude of each third dihedral angle error is greater than 1 degree.

Embodiment 28: An embodiment of any embodiment of embodiments 25-27,wherein the magnitude of the average of the first dihedral angle errorsis less than 0.3 degrees, wherein the magnitude of the average of thesecond dihedral errors is less than 0.3 degrees, and wherein the averageof the third dihedral angle errors is less than −1 degrees.

Embodiment 29: An embodiment of any embodiment of embodiments 22-28,wherein each of the retroreflective elements comprises a non-equilateraltriangular pyramid prism bounded by one of a first set of substantiallyparallel and v-shaped first grooves, one of a second set ofsubstantially parallel and v-shaped second grooves, and one of a thirdset of substantially parallel and v-shaped third grooves; whereinadjacent first grooves are separated by a first spacing ranging from 0.1mm to 0.2 mm; wherein adjacent second grooves are separated by a secondspacing substantially identical to the first spacing; and whereinadjacent third grooves are separated by a third spacing smaller than thefirst and second spacing.

Embodiment 30: An embodiment of any embodiment of embodiments 22-29,wherein the depth of each prism ranges from 1 mil to 5 mils.

Embodiment 31: An embodiment of any embodiment of embodiments 22-30,wherein the each prism is canted face-more-parallel.

Embodiment 32: An embodiment of embodiment 31, wherein each prism iscanted at a cant angle ranging from −5 degrees to −8 degrees.

Embodiment 33: An embodiment of any embodiment of embodiments 22-30,wherein each prism is canted edge-more-parallel.

Embodiment 34: An embodiment of embodiment 33, wherein each prism iscanted at a cant angle ranging from 5 degrees to 8 degrees.

Embodiment 35: An embodiment of any embodiment of embodiments 22-34,further comprising: a diffusing film having a full-width half-maximumangle of diffusion of less than 1 degree in a horizontal x directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.

Embodiment 36: An embodiment of any embodiment of embodiments 22-34,further comprising: a diffusing film having a full-width half-maximumangle of diffusion of greater than 3 degrees in a vertical y directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.

Embodiment 37: An embodiment of any embodiment of embodiments 22-34,further comprising: a diffusing film having: (1) a full-widthhalf-maximum angle of diffusion of less than 1 degree in a horizontalx-direction substantially parallel to the front surface of theretroreflective film when the front and back surfaces of theretroreflective film are positioned vertically, and (2) a full-widthhalf-maximum angle of diffusion of greater than 3 degrees in a verticaly-direction substantially parallel to the front surface of theretroreflective film when the front and back surfaces of theretroreflective film are positioned vertically.

Embodiment 38: An embodiment of any embodiment of embodiments 35-37,wherein the diffusing film is directly adjacent to the front surface ofthe retroreflective film.

Embodiment 39: An embodiment of any embodiment of embodiments 22-38,wherein the retroreflective film comprises acrylic or polycarbonate.

Embodiment 40: An embodiment of any embodiment of embodiments 22-39,wherein each of the retroreflective elements are air-backed.

Embodiment 41: An embodiment of any embodiment of embodiments 22-40,wherein the retroreflective article is a display screen.

Embodiment 42: A retroreflective article comprising: a retroreflectivefilm comprising opposing front and back surfaces; and a plurality ofretroreflective elements disposed on the back surface of theretroreflective film; wherein each of the retroreflective elementscomprises a non-equilateral triangular pyramid prism having a thirddihedral angle error less than −1 degrees; wherein each prism is boundedby one of a first set of substantially parallel and v-shaped firstgrooves, one of a second set of substantially parallel and v-shapedsecond grooves, and one of a third set of substantially parallel andv-shaped third grooves; wherein each of the grooves comprises a grooveaxis and two intersecting groove sides; wherein each groove side of agroove forms a half angle between the groove side and a plane parallelto the groove axis of the groove and orthogonal to the back surface ofthe retroreflective film; and wherein at least one of the half anglesranges from 25 degrees to 30 degrees.

Embodiment 43: An embodiment of embodiment 42, wherein the thirddihedral angle ranges from −1 degrees to −4 degrees.

Embodiment 44: An embodiment of embodiment 42 or 43, further comprising:a diffusing film having: (1) a full-width half-maximum angle ofdiffusion of greater than 1 degree in a horizontal x-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically, and (2) a full-width half-maximum angle ofdiffusion of greater than 3 degrees in a vertical y-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.

Embodiment 45: An embodiment of embodiment 44, wherein the diffusingfilm is directly adjacent to the front surface of the retroreflectivefilm.

Embodiment 46: An embodiment of any embodiment of embodiments 42-45,wherein each of the retroreflective elements comprises a first, second,and third triangular face; wherein the first, second, and thirdtriangular faces intersect at an apex configured to point away from theback surface; wherein the first and second triangular faces aresubstantially congruent triangles; and wherein the third triangular faceis not congruent with the first and second triangular faces.

Embodiment 47: An embodiment of any embodiment of embodiments 42-46,wherein adjacent first grooves are separated by a first spacing rangingfrom 0.1 mm to 0.2 mm; wherein adjacent second grooves are separated bya second spacing substantially identical to the first spacing; andwherein adjacent third grooves are separated by a third spacing largerthan the first and second spacing.

Embodiment 48: An embodiment of any embodiment of embodiments 42-47,wherein the depth of each prism ranges from 1 mil to 5 mils.

Embodiment 49: An embodiment of any embodiment of embodiments 42-48,wherein each prism is canted edge-more-parallel at a cant ranging from 4degrees to 10 degrees.

Embodiment 50: An embodiment of any embodiment of embodiments 42-49,wherein the retroreflective film comprises acrylic or polycarbonate.

Embodiment 51: An embodiment of any embodiment of embodiments 42-50,wherein each of the retroreflective elements are air-backed.

Embodiment 52: An embodiment of any embodiment of embodiments 42-51,wherein the retroreflective article is a display screen.

Embodiment 53: A retroreflective article comprising: a retroreflectivefilm comprising opposing front and back surfaces; and a plurality ofretroreflective elements disposed on the back surface of theretroreflective film; wherein each of the retroreflective elementscomprises a non-equilateral triangular pyramid prism bounded by one of afirst set of substantially parallel and v-shaped first grooves, one of asecond set of substantially parallel and v-shaped second grooves, andone of a third set of substantially parallel and v-shaped third grooves;wherein each of the grooves comprises a groove axis and two intersectinggroove sides; wherein each groove side of a groove forms a half anglebetween the groove side and a plane parallel to the groove axis of thegroove and orthogonal to the back surface of the retroreflective film;wherein at least one of the half angles ranges from 25.0 degrees to 30.0degrees; and wherein each prism is canted edge-more-parallel at a cantangle greater than 0 degrees.

Embodiment 54: An embodiment of embodiment 53, wherein each prism iscanted at a cant angle ranging from 4 degrees to 10 degrees.

Embodiment 55: An embodiment of embodiment 53 or 54, further comprising:a diffusing film having: (1) a full-width half-maximum angle ofdiffusion of greater than 1 degree in a horizontal x-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically, and (2) a full-width half-maximum angle ofdiffusion of greater than 3 degrees in a vertical y-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.

Embodiment 56: An embodiment of embodiment 55, wherein the diffusingfilm is directly adjacent to the front surface of the retroreflectivefilm.

Embodiment 57: An embodiment of any embodiment of embodiments 53-56,wherein each of the retroreflective elements comprises a first, second,and third triangular face; wherein the first, second, and thirdtriangular faces intersect at an apex configured to point away from theback surface; wherein the first and second triangular faces aresubstantially congruent triangles; and wherein the third triangular faceis not congruent with the first and second triangular faces.

Embodiment 58: An embodiment of any embodiment of embodiments 53-57,wherein each prism has a third dihedral angle error ranging from −4degrees to −1 degrees.

Embodiment 59: An embodiment of any embodiment of embodiments 53-58,wherein adjacent first grooves are separated by a first spacing rangingfrom 0.1 mm to 0.2 mm; wherein adjacent second grooves are separated bya second spacing substantially identical to the first spacing; andwherein adjacent third grooves are separated by a third spacing largerthan the first and second spacing.

Embodiment 60: An embodiment of any embodiment of embodiments 53-59,wherein the depth of each prism ranges from 1 mil to 5 mils.

Embodiment 61: An embodiment of any embodiment of embodiments 53-60,wherein the retroreflective film comprises acrylic or polycarbonate.

Embodiment 62: An embodiment of any embodiment of embodiments 53-61,wherein each of the retroreflective elements are air-backed.

Embodiment 63: An embodiment of any embodiment of embodiments 53-62,wherein the retroreflective article is a display screen.

Embodiment 64: A display system comprising: the retroreflective articleof any embodiment of embodiments 1-63; a projector configured to directan incident light beam towards the retroreflective article; and acomputer processor operatively connected with a machine-readablenon-transitory medium embodying information indicative of instructionsfor causing the computer processor to perform operations comprisingcontrolling the projector to direct the incident light beam towards theretroreflective article; wherein the retroreflective article isconfigured to reflect the incident light beam such that the majority ofreflected light is divided into (1) a first reflected light beam offsetfrom the incident light beam by a first reflected angle greater than 1degree, and (2) a second reflected light beam offset from the incidentlight beam by a second reflected angle having a magnitude substantiallyidentical to that of the first reflected angle and a direction oppositethat of the first reflected angle relative to the incident light beam.

Embodiment 65: An embodiment of embodiment 64, wherein the firstreflected angle is greater than 4 degrees above the incident light beam,and the second reflected angle is greater than 4 degrees below theincident light beam, when the front and back surfaces of theretroreflective film are positioned vertically.

Embodiment 66: An embodiment of embodiment 64 or 65, wherein the firstreflected light beam has a first brightness, and wherein the secondreflected light beam has a second brightness substantially identical tothat of the first reflected light beam.

Embodiment 67: A method of displaying an image, the method comprising:providing a retroreflective article of any embodiment of embodiments1-63; providing a projector; and controlling the projector to direct anincident light beam towards the retroreflective article, therebyreflecting the incident light beam into (1) a first reflected light beamoffset from the incident light beam by a first reflected angle greaterthan 1 degree, and (2) a second reflected light beam offset from theincident light beam by a second reflected angle having a magnitudesubstantially identical to that of the first reflected angle and adirection opposite that of the first reflected angle relative to theincident light beam.

Embodiment 68: An embodiment of embodiment 67, wherein the firstreflected angle is greater than 4 degrees above the incident light beam,and the second reflected angle is greater than 4 degrees below theincident light beam, when the front and back surfaces of theretroreflective film are positioned vertically.

Embodiment 69: An embodiment of embodiment 67 or 68, wherein the firstreflected light beam has a first brightness, and wherein the secondreflected light beam has a second brightness substantially identical tothat of the first reflected light beam.

EXAMPLES

The present disclosure will be better understood in view of thefollowing non-limiting example. An exemplary retroreflective articleincludes three sets of parallel grooves cut into an acrylic film. Thegrooves of the first set have half angles of 29.67 degrees and 29.14degrees, and are separated from one another by a spacing of 0.142 mm.The grooves of the second set also have half angles of 29.67 degrees and29.14 degrees, and are separated from one another by a spacing of 0.142mm. The grooves of the third set have half angles of 44.55 degrees and44.33 degrees, and are separated from one another by a spacing of 0.128mm. Together the grooves create cube corner retroreflective elementshaving a cube corner depth of 2.5 mils, and a cube cant of approximately−6.5 degrees (or 6.5 degrees face-more-parallel). The individual cubecorner elements belong to one of eight groups, depending on thebordering groove half angles. Dimensions, including dihedral angles foreach of the eight groups are shown in Table 1 below.

TABLE 1 Cube Corner Dimensions Half Half Half Dihedral Dihedral Dihedralgroove groove groove angle angle angle Cube angle angle angle errorerror error corner HG₁ (°) HG₂ (°) HG₃ (°) e₁ (°) e₂ (°) e₃ (°) 1 29.6729.67 44.55 0.33 0.33 −2.55 2 29.67 29.67 44.33 0.18 0.18 −2.55 3 29.6729.14 44.55 −0.10 0.33 −2.87 4 29.67 29.14 44.33 −0.25 0.18 −2.87 529.14 29.67 44.55 0.33 −0.10 −2.87 6 29.14 29.67 44.33 0.18 −0.25 −2.877 29.14 29.14 44.55 −0.10 −0.10 −3.18 8 29.14 29.14 44.33 −0.25 −0.25−3.18 Avg 29.41 29.41 44.44 0.04 0.04 −2.87

As shown in Table 1, cube corners 1 and 8 both have first and seconddihedral angle errors that are identical to one another. Furthermore,the first and second dihedral angle errors of cube corner 1 have acomparable magnitude and opposite sign to the first and second dihedralangle errors of cube corner 8. Also, the average of the first dihedralangle errors of the eight cube corners, as well as the average of thesecond dihedral angle errors of the eight cube corners, is close tozero. This indicates that the configuration of the retroreflectiveelement array is substantially balanced. Such a balanced configurationhas been shown to provide a more symmetrical light beam profile, such asthose of FIGS. 1-3.

In contrast, if the averages of the first and/or second dihedral angleerrors have magnitudes significantly greater than zero, as shown inTable 2 below, then the profile can become more asymmetrical. This isthe case for the profiles of FIG. 11, which represent light beampositions for a retroreflective article having more positive averagefirst and second dihedral angle errors. The change in width for the FIG.11 light beam profiles with respect to height can provide some benefitsfor certain applications, although in general more symmetrical profilesare preferred.

TABLE 2 Cube Corner Dimensions for FIG. 11 Half Half Half DihedralDihedral Dihedral groove groove groove angle angle angle Cube angleangle angle error error error corner HG₁ (°) HG₂ (°) HG₃ (°) e₁ (°) e₂(°) e₃ (°) 1 29.71 29.71 45.07 0.67 0.67 −2.55 2 29.71 29.71 44.85 0.510.51 −2.55 3 29.71 29.17 45.07 0.24 0.67 −2.87 4 29.71 29.17 44.85 0.080.51 −2.87 5 29.17 29.71 45.07 0.67 0.24 −2.87 6 29.17 29.71 44.85 0.510.08 −2.87 7 29.17 29.17 45.07 0.24 0.24 −3.18 8 29.14 29.17 44.85 0.080.08 −3.18 Avg 29.44 29.44 44.96 0.37 0.37 −2.87

While the embodiments have been described in detail, modificationswithin the spirit and scope of the disclosure will be readily apparentto those of skill in the art. In view of the foregoing discussion,relevant knowledge in the art and references discussed above inconnection with the Background and Detailed Description, the disclosuresof which are all incorporated herein by reference. In addition, itshould be understood that aspects of the disclosure and portions ofvarious embodiments and various features recited below and/or in theappended claims may be combined or interchanged either in whole or inpart. In the foregoing descriptions of the various embodiments, thoseembodiments which refer to another embodiment may be appropriatelycombined with other embodiments as will be appreciated by one of skillin the art. Furthermore, those of ordinary skill in the art willappreciate that the foregoing description is by way of example only, andis not intended to limit the disclosure.

We claim:
 1. A retroreflective article comprising: a retroreflectivefilm comprising opposing front and back surfaces; and a plurality ofretroreflective elements disposed on the back surface of theretroreflective film; wherein each of the retroreflective elementscomprises a non-equilateral triangular pyramid prism bounded by one of afirst set of substantially parallel and v-shaped first grooves, one of asecond set of substantially parallel and v-shaped second grooves, andone of a third set of substantially parallel and v-shaped third grooves;wherein each of the grooves comprises a groove axis and two intersectinggroove sides; wherein each groove side of a groove forms a half anglebetween the groove side and a plane parallel to the groove axis of thegroove and orthogonal to the back surface of the retroreflective film;and wherein at least one of the half angles ranges from 25.0 degrees to28.5 degrees, or ranges from 43.5 degrees to 45.0 degrees.
 2. Theretroreflective article of claim 1, wherein each prism has a first,second, and third dihedral angle error; and wherein the magnitude ofeach dihedral angle error ranges from 0.01 degrees to 10 degrees.
 3. Theretroreflective article of claim 2, wherein the magnitude of each thirddihedral angle error is greater than 1 degree.
 4. The retroreflectivearticle of claim 2, wherein the magnitude of the average of the firstdihedral angle errors is less than 0.3 degrees, wherein the magnitude ofthe average of the second dihedral errors is less than 0.3 degrees, andwherein the average of the third dihedral angle errors is less than −1degrees.
 5. The retroreflective article of claim 1, wherein adjacentfirst grooves are separated by a first spacing ranging from 0.1 mm to0.2 mm; wherein adjacent second grooves are separated by a secondspacing substantially identical to the first spacing; and whereinadjacent third grooves are separated by a third spacing smaller than thefirst and second spacing.
 6. The retroreflective article of claim 1,wherein the depth of each prism ranges from 1 mil to 5 mils.
 7. Theretroreflective article of claim 1, wherein each prism is cantedface-more-parallel at a cant angle ranging from −5 degrees to −8degrees.
 8. The retroreflective article of claim 1, wherein each prismis canted edge-more-parallel at a cant angle ranging from 4 degrees to 8degrees.
 9. The retroreflective article of any claim 1, furthercomprising: a diffusing film having: (1) a full-width half-maximum angleof diffusion of less than 1 degree in a horizontal x-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically, and (2) a full-width half-maximum angle ofdiffusion of greater than 3 degrees in a vertical y-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.
 10. A retroreflective article comprising: aretroreflective film comprising opposing front and back surfaces; and aplurality of retroreflective elements disposed on the back surface ofthe retroreflective film; wherein each of the retroreflective elementsis a non-equilateral triangular pyramid prism comprising a triangularbase; and wherein the triangular base comprises two sides that differ inlength from one another such that the ratio of the length of the smallerof the two sides to the length of the larger of the two sides rangesfrom 80% to 92.5%.
 11. The retroreflective article of claim 10, whereineach prism has a first, second, and third dihedral angle error; andwherein the magnitude of each dihedral angle error ranges from 0.01degrees to 10 degrees.
 12. The retroreflective article of claim 11,wherein the magnitude of each third dihedral angle error is greater than1 degree.
 13. The retroreflective article of claim 11, wherein themagnitude of the average of the first dihedral angle errors is less than0.3 degrees, wherein the magnitude of the average of the second dihedralerrors is less than 0.3 degrees, and wherein the average of the thirddihedral angle errors is less than −1 degrees.
 14. The retroreflectivearticle of claim 10, wherein each of the retroreflective elementscomprises a non-equilateral triangular pyramid prism bounded by one of afirst set of substantially parallel and v-shaped first grooves, one of asecond set of substantially parallel and v-shaped second grooves, andone of a third set of substantially parallel and v-shaped third grooves;wherein adjacent first grooves are separated by a first spacing rangingfrom 0.1 mm to 0.2 mm; wherein adjacent second grooves are separated bya second spacing substantially identical to the first spacing; andwherein adjacent third grooves are separated by a third spacing smallerthan the first and second spacing.
 15. The retroreflective article ofclaim 10, wherein the depth of each prism ranges from 1 mil to 5 mils.16. The retroreflective article of claim 10, wherein each prism iscanted face-more-parallel at a cant angle ranging from −5 degrees to −8degrees.
 17. The retroreflective article of claim 10, wherein each prismis canted edge-more-parallel at a cant angle ranging from 4 degrees to 8degrees.
 18. The retroreflective article of claim 10, furthercomprising: a diffusing film having: (1) a full-width half-maximum angleof diffusion of less than 1 degree in a horizontal x-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically, and (2) a full-width half-maximum angle ofdiffusion of greater than 3 degrees in a vertical y-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.
 19. A retroreflective article comprising:. aretroreflective film comprising opposing front and back surfaces; and aplurality of retroreflective elements disposed on the back surface ofthe retroreflective film; wherein each of the retroreflective elementscomprises a non-equilateral triangular pyramid prism having a thirddihedral angle error with a magnitude greater than 1 degree; whereineach prism is bounded by one of a first set of substantially paralleland v-shaped first grooves, one of a second set of substantiallyparallel and v-shaped second grooves, and one of a third set ofsubstantially parallel and v-shaped third grooves; wherein each of thegrooves comprises a groove axis and two intersecting groove sides;wherein each groove side of a groove forms a half angle between thegroove side and a plane parallel to the groove axis of the groove andorthogonal to the back surface of the retroreflective film; and whereinat least one of the half angles ranges from 25 degrees to 30 degrees.20. The retroreflective article of claim 19, wherein the third dihedralangle ranges from −1 degrees to −4 degrees.
 21. The retroreflectivearticle of claim 19, further comprising: a diffusing film having: (1) afull-width half-maximum angle of diffusion of greater than 1 degree in ahorizontal x-direction substantially parallel to the front surface ofthe retroreflective film when the front and back surfaces of theretroreflective film are positioned vertically, and (2) a full-widthhalf-maximum angle of diffusion of greater than 3 degrees in a verticaly-direction substantially parallel to the front surface of theretroreflective film when the front and back surfaces of theretroreflective film are positioned vertically.
 22. The retroreflectivearticle of claim 19, wherein adjacent first grooves are separated by afirst spacing ranging from 0.1 mm to 0.2 mm; wherein adjacent secondgrooves are separated by a second spacing substantially identical to thefirst spacing; and wherein adjacent third grooves are separated by athird spacing larger than the first and second spacing.
 23. Theretroreflective article of claim 19, wherein the depth of each prismranges from 1 mil to 5 mils.
 24. The retroreflective article of claim19, wherein each prism is canted edge-more-parallel at a cant rangingfrom 4 degrees to 10 degrees.
 25. A retroreflective article comprising:a retroreflective film comprising opposing front and back surfaces; anda plurality of retroreflective elements disposed on the back surface ofthe retroreflective film; wherein each of the retroreflective elementscomprises a non-equilateral triangular pyramid prism bounded by one of afirst set of substantially parallel and v-shaped first grooves, one of asecond set of substantially parallel and v-shaped second grooves, andone of a third set of substantially parallel and v-shaped third grooves;wherein each of the grooves comprises a groove axis and two intersectinggroove sides; wherein each groove side of a groove forms a half anglebetween the groove side and a plane parallel to the groove axis of thegroove and orthogonal to the back surface of the retroreflective film;wherein at least one of the half angles ranges from 25.0 degrees to 30.0degrees; and wherein each prism is canted edge-more-parallel at a cantangle greater than 0 degrees.
 26. The retroreflective article of claim25, wherein each prism is canted at a cant angle ranging from 4 degreesto 10 degrees.
 27. The retroreflective article of claim 25, furthercomprising: a diffusing film having: (1) a full-width half-maximum angleof diffusion of greater than 1 degree in a horizontal x-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically, and (2) a full-width half-maximum angle ofdiffusion of greater than 3 degrees in a vertical y-directionsubstantially parallel to the front surface of the retroreflective filmwhen the front and back surfaces of the retroreflective film arepositioned vertically.
 28. The retroreflective article of claim 25,wherein each prism has a third dihedral angle error ranging from −4degrees to −1 degrees.
 29. The retroreflective article of claim 25,wherein adjacent first grooves are separated by a first spacing rangingfrom 0.1 mm to 0.2 mm; wherein adjacent second grooves are separated bya second spacing substantially identical to the first spacing; andwherein adjacent third grooves are separated by a third spacing largerthan the first and second spacing.
 30. The retroreflective article ofclaim 25, wherein the depth of each prism ranges from 1 mil to 5 mils.31. A display system comprising: the retroreflective article of claim 1;a projector configured to direct an incident light beam towards theretroreflective article; and a computer processor operatively connectedwith a machine-readable non-transitory medium embodying informationindicative of instructions for causing the computer processor to performoperations comprising controlling the projector to direct the incidentlight beam towards the retroreflective article; wherein theretroreflective article is configured to reflect the incident light beamsuch that the majority of reflected light is divided into (1) a firstreflected light beam offset from the incident light beam by a firstreflected angle greater than 1 degree, and (2) a second reflected lightbeam offset from the incident light beam by a second reflected anglehaving a magnitude substantially identical to that of the firstreflected angle and a direction opposite that of the first reflectedangle relative to the incident light beam.
 32. The display system ofclaim 31, wherein the first reflected angle is greater than 4 degreesabove the incident light beam, and the second reflected angle is greaterthan 4 degrees below the incident light beam, when the front and backsurfaces of the retroreflective film are positioned vertically.
 33. Amethod of displaying an image, the method comprising: providing aretroreflective article of claim 1; providing a projector; andcontrolling the projector to direct an incident light beam towards theretroreflective article, thereby reflecting the incident light beam into(1) a first reflected light beam offset from the incident light beam bya first reflected angle greater than 1 degree, and (2) a secondreflected light beam offset from the incident light beam by a secondreflected angle having a magnitude substantially identical to that ofthe first reflected angle and a direction opposite that of the firstreflected angle relative to the incident light beam.
 34. The method ofclaim 33, wherein the first reflected angle is greater than 4 degreesabove the incident light beam, and the second reflected angle is greaterthan 4 degrees below the incident light beam, when the front and backsurfaces of the retroreflective film are positioned vertically.